Existence of a semilinear elliptic system with exponential nonlinearities

Abstract

We consider a system of semilinear elliptic partial different equations with exponential nonlinearities in R-2. We construct a solution of the system viewing the system as a perturbation of the decoupled Liousville equations and applying suitable implicit function theorem. As a byproduct we obtain very precise information on the asymptotic behaviors of the solutions near infinity.